Here's the most recent thread on the oldest courses in the U.S.:
http://www.golfclubatlas.com/forum/index.php/topic,54616.0.htmlThe list currently looks like this:
1886
The Dorset Field Club, Dorset, VT
1887
The Foxburg Country Club, Foxburg, PA
Quogue Field Club, Long Island, NY
1888
The Saint Andrew's Club, Hastings-on-Hudson, New York
1889
The Country Club of Middlesboro, KY. - 9 holes.
The Tuxedo Club, Tuxedo Park, NY (relocated)
1890
The Dutcher Golf Course, Pawling, NY – 9 holes
1891
Shinnecock Hills, Southampton, NY
Aetna Springs, Pope Valley, CA
Grindstone Neck, Winter Harbor, ME – 9 holes
Kebo Valley Golf Club, Bar Harbor, ME
Gearhart Golf Links, Gearhart, OR
Cheyenne Mountain Golf Club, Colorado Springs, CO
1892
Highland Links Golf Course, Cape Cod, MA – 9 holes
The Downers Grove Golf Club, Downers Grove, IL
The Old Course at the Homestead, Hot Springs, VA
Palmetto Golf Club, Aiken, SC
Mare Island Golf Club, Vallejo, California
Moorestown Field Club, Moorestown, NJ – 9 holes
Merchantville Country Club, Cherry Hill, NJ – 9 holes
1893
The Town & Country Club, St. Paul, MN
The Country Club, Brookline, MA